UC Berkeley UC Berkeley Electronic Theses and Dissertations Title Geometry, Dynamics, and Emergence: Cowrie Form, Image Geometry, and Coupled Subcritical Oscillations Permalink https://escholarship.org/uc/item/8rd8n022 Author Levy, Michael Gabriel Publication Date 2019 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California Geometry, Dynamics, and Emergence: Cowrie Form, Image Geometry, and Coupled Subcritical Oscillations by Michael Gabriel Levy A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Biophysics in the Graduate Division of the University of California, Berkeley Committee in charge: Associate Professor Michael Robert DeWeese, Chair Professor Bruno Olshausen Associate Professor Oskar Halletschk Fall 2019 Geometry, Dynamics, and Emergence: Cowrie Form, Image Geometry, and Coupled Subcritical Oscillations Copyright 2019 by Michael Gabriel Levy 1 Abstract Geometry, Dynamics, and Emergence: Cowrie Form, Image Geometry, and Coupled Subcritical Oscillations by Michael Gabriel Levy Doctor of Philosophy in Biophysics University of California, Berkeley Associate Professor Michael Robert DeWeese, Chair Living Systems are dynamically controlled by processes that they themselves create: here we study the emergence of the sophisticated control regimes in models of biological systems. A major route to understanding in Biology today is discovering which genes lead to what, almost always neglecting a story for how the genes achieve their ends. From an understand- ing perspective this is disappointing, and we strive to make more holistic models which try to get at the underlying nature of biological logic. Towards this end, we notice geometric regimes in cowrie growth and work towards a falsifiable and explanatory mechanistic model, aiming to make the case for the importance of mechanics and dynamics in development. We also present the first systematic study of globally-coupled subcritical limit cycle oscillators, exploring a rarely remarked upon dynamical regime. This regime is biologically interesting as it has bistability between oscillations and quiescence and is a simple excitable media which could be used as a reduced neural model. I am interested in clustering in the system as an example of symmetry breaking in identical systems; small differences in initial conditions lead to differentiation of the oscillators into particular varieties, analogous to cell fate de- cisions. Progress on these problems works towards illuminating the biological approach to self-assembly. i To those that did not survive this dissertation George F. Oster and Harold Lecar and Nico Linesh May this work do honor to your lives and legacy. ii Contents Contents ii 1 Dynamics and Aims 1 1.1 Emergence and Model Levels . 1 1.2 Why Chimeras? . 2 1.3 Why Cowrie Seashells? . 2 1.4 Dynamics: Bifurcation, Continuation, and Chaos . 3 2 Dynamics of Linearly Coupled Subcritical Oscillatators 5 2.1 Introduction to and Motivation for Equations . 5 2.2 Linear Stability of Synchronized and Splay States . 10 2.3 Empirical Bifurcation Plots and Unbalanced Optimal Transport . 18 2.4 Conclusions and Synthesis . 22 3 Image Geometry and Dynamics: Information Extraction and Seashell Pattern 23 3.1 Geometric Approaches to Image Analysis . 23 3.2 Splines and Active Contours . 24 3.3 Seashell Pattern Generation . 25 3.4 Conclusions and Synthesis . 40 4 Cowrie Shape and Form 41 4.1 Introduction . 41 4.2 Cowrie Shell Observables . 43 4.3 Extracting Relevant Data . 49 4.4 Towards Models of Cowrie Growth . 52 4.5 The Physics of Wrinkling Sheets . 56 4.6 Model consolidation and a Coherent Story of Cowrie Form . 57 5 Conclusions 58 5.1 Future Directions . 58 Bibliography 59 iii Acknowledgments I would like to thank Edgar Knobloch for his patience and Michael DeWeese for his support. I would like to thank Dawn Song, George Oster, Padmini Rangamani, George Roderick and the ESPM Department, the NIH, the NSF, and the Cognitive Science, Physics, and Bioengineering Departments, Joseph Levy, and Leslie Feinberg for funding. I would like to thank Kate Chase and Susan Marqusee and the rest of the Biophysics Graduate Group for providing \enough rope to hang" myself and enough time to get myself untangled. I would like to thank HiP House and the Berkeley Student Cooperative: without this afford- able housing option (and community) I would have dropped out long ago. I want to thank Terry Regier of Cog Sci and Holger Meuller and Hilary Jacks of Physics for giving me the opportunity to teach classes of my own design. I want to thank the Compass Project for experience teaching | both students and teachers | and providing a network of similarly minded folk to think with. I would like to thank\math club" in all its iterations: Paul Glenn, Danny Broberg, Michelle Liu, and Ben Larson; Lunch Buddies Madeline Forester, Vanessa Carels, Sam Harding-Forester, Brian Isett, Ben McInroe, Ben Forester, and Alex Takeda. I would like to thank MCB/Neuroscience for the many faculty lunches they took me out to; and UC Berkeley, MBI at the Ohio State University, and The Champaulimaud Center for the Unknown for travel funds; and to thank Punit Ghandi, Kelly Clancey, Jacque Bothma, Jasmine Nirody, Aisha Wilson, Amy Shyer, Neha Wadia, Ryan Zarcone, Gautum Agar- wal, Jasha Sohl-Dickstein, Jean-Michel Mongeau, Alistair Boettiger, Kranthi Mandadapu, Padmini Rangamani, Richard Barnes, Anna Schnider, Julian Hassinger, John Haberstroh, Jesse Livzey, Michael Grabe, Ken Kim, John Neu, and the greater Biophysics/George Oster community for whatever I have gleaned purposely or in passing. I would like to thank Fred- erick Theunissen, Dan Rockshar, Udi Isacoff, and Philip Geissler for rotation projects, and Richard Kramer, Bruno Olshausen, Oskar Halletchk, David Lindberg, the Architecture Fab Lab, the geology department rock cutting facility, and David Stiegmann for their time and interest. I would like to greatly acknowledge George Oster and Harold Lecar for giving what they could. I would like to acknowledge Gloria Lee, Devyn Shafer, and | most importantly | Sarah Alice McCracken for the connection, tethering, and growth they fostered. I would like to thank the place and the tenor of Berkeley California for all I've learned from living here and I would like to acknowledge my family and friends for their unwavering support particularly my brother and sister Joshua and Rebecca Levy. Finally, I would like to ac- knowledge my aforementioned parents Joseph and Leslie: I wouldn't be let alone be a PhD without your support. Thank you fam: we made it. 1 Chapter 1 Dynamics and Aims 1.1 Emergence and Model Levels Cognitive Science has a conceptual frame that they refer to as Marr's Levels[12], which con- tends there are three ways one can attack understanding a system: at the conceptual level, at the algorithm and representation level, and at the implementation level. This distinction is epistomologically helpful and is intellectually satisfying for someone not incredibly interested in molecular detail. Interestingly, following the tendency for things not to be named after their originator, this conceptual distinction was discussed in its entirety many years before by Shannon[21], and feels like good common sense in the\more is different" vein [3]. The distinction is as follows: when one is seeking to understand something there are basically three questions one can ask: Why, How, and What. The Why is the conceptual level which involves evolutionary and optimization arguments. The How is the level of emergence, con- densed matter, and statistical physics which tries to link microscopic details to macroscopic phenomena. In the cognitive frame, this would be how is information manipulated and stored in the wetware that is your brain to lead to percepts, conciousness, and whatnot. This is the level which I find most intellectually satisfying, as it avoids the \just so" stories of the level above it and the particular details of the level below it. The implementation level is the level of molecular Neuroscience, how do individual cells encode information, very specifically which molecules do what when. I find this level incredibly interesting yet overwhelming { the torrent of information and details at this level seems to get in the way of understanding, the ol' seeing the forrest for the trees. This reminds of Poincare's dictum \on fait la science avec des faits comme une maison avec des pierres ; mais une accumulation de faits n'est pas plus une science qu'un tas de pierres n'est une maison." |Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house. It is the goal of this thesis to provide some tools engaging with the algorithmic layer, codifying models that provide hypotheses, synthesizing and predicting implentational details, and providing constraints on the computational possibilities. CHAPTER 1. DYNAMICS AND AIMS 2 1.2 Why Chimeras? Chimeras are a strange situation where chaotic motion and synchronization coexist in iden- tical oscillators[1]. The usual reported biological motivation for studying this state is uni- hemispheric sleep and study of this state emerged from the study of synchronizing oscillators, a quintessential biophysical endeavor[4]. This state, which has since its discovery been shown to be realizable in many physical systems, is an example of a state whose components have only a dynamical identity. The only thing different